Next Eigenvalue Sufficiency Test.

Rnest: An R package for the Next Eigenvalue Sufficiency Test

The library Rnest offers the Next Eigenvalue Sufficiency Tests (NEST) (Achim, 2017, 2020) to determine the number of dimensions in exploratory factor analysis. It provides a main function nest() to carry the analysis and a plot() function.

There is also many examples of correlation matrices available with the packages and other stopping rules as well, such as pa() for parellel analysis.

Installation

The development version can be accessed through GitHub:

remotes::install_github(repo = "quantmeth/Rnest")
library(Rnest)

Examples

Here is an example using the ex_4factors_corr correlation matrix from the Rnest library. The factor structure is

and the correlation matrix is

$$\begin{bmatrix} 1&0.81&0.27&0.567&0.567&0.189&0&0&0&0&0&0 \
0.81&1&0.27&0.567&0.567&0.189&0&0&0&0&0&0 \
0.27&0.27&1&0.189&0.189&0.063&0&0&0&0&0&0 \
0.567&0.567&0.189&1&0.81&0.27&0&0&0&0&0&0 \
0.567&0.567&0.189&0.81&1&0.27&0&0&0&0&0&0 \
0.189&0.189&0.063&0.27&0.27&1&0&0&0&0&0&0 \
0&0&0&0&0&0&1&0.81&0.27&0.567&0.567&0.189 \
0&0&0&0&0&0&0.81&1&0.27&0.567&0.567&0.189 \
0&0&0&0&0&0&0.27&0.27&1&0.189&0.189&0.063 \
0&0&0&0&0&0&0.567&0.567&0.189&1&0.81&0.27 \
0&0&0&0&0&0&0.567&0.567&0.189&0.81&1&0.27 \
0&0&0&0&0&0&0.189&0.189&0.063&0.27&0.27&1 \
\end{bmatrix}$$

From ex_4factors_corr, we can easily generate random data using the MASS packages (Venables & Ripley, 2002).

set.seed(1)
mydata <- MASS::mvrnorm(n = 2500,
                        mu = rep(0, ncol(ex_4factors_corr)),
                        Sigma = ex_4factors_corr)

We can then carry NEST.

res <- nest(mydata)
res

## At 95% confidence, Nest Eigenvalue Sufficiency Test (NEST) suggests 4 factors.

The first output tells hom many factors NEST suggest. We can also consult the summary with

summary(res)

## 
## nest 0.0.0.1 ended normally 
##  
##    Estimator                       ML 
##    Number of model parameters      66 
##    Resampling                      1000 
##    Sample size                     2500 
##    Stopped at                      5 
##  
##  
## Probabilities of factors 
##   Factor     Eigenvalue     Prob 
##     F1         3.228       < .001 
##     F2         3.167       < .001 
##     F3         1.007         .009 
##     F4         0.972         .009 
##     F5         0.860         .735 
## 
##  
## At 95% confidence, Nest Eigenvalue Sufficiency Test (NEST) suggests 4 factors. 
## Try plot(nest()) to see a graphical representation of the results. 
## 

We can visualize the results using the generic function plot() using the nest() output.

plot(res)

The above figure shows the empirical eigenvalues in blue and the 95^th percentile of the sampled eigenvalues.

It is also possible to use a correlation matrix directly. A sample size, n must be supplied.

nest(ex_4factors_corr, n = 240)

## At 95% confidence, Nest Eigenvalue Sufficiency Test (NEST) suggests 2 factors.

The nest() function can use with many $\alpha$ values if desired.

res <- nest(ex_4factors_corr, n = 120, alpha = c(.01,.025,.05,.1))
plot(res)

How to cite

Caron, P.-O. (2023). Rnest: An R package for the Next Eigenvalue Sufficiency Test. https://github.com/quantmeth/Rnest

References